Dr. Tarakanta NayakAssociate Professor
School of Basic Sciences

Research Interests

Complex Dynamics; Fractals; Independence polynomials and Independent fractals of graphs

Contact Details

  • 329, SBS Building
  • 674-713-5166
  • tnayakATiitbbsDOTacDOTin

Other Profile Link(s)

Education

 Degree Discipline Year School
 Ph.D. Mathematics 2001-2006 Indian Institute of Technology Guwahati
 Post doc Mathematics 2008-2009 School of Mathematical Sciences, Tsinghua University, Beijing
 

Biosketch

 Born and brought up in a remote village called Raisar in the Kendrapda district of Odisha. Schooling in the village school and college study in Salipur College, affiliated to the Utkal University, Bhubaneswar. After completing MSc in Mathematics in the Utkal University, I moved to IIT Guwahati for PhD,
 
 

Teaching

Math-I, Math-II, Transform Calculus, Probability, Statistics & Stochastic Processes, Complex Analysis, Fractals, Advanced Complex Analysis, Complex Dynamics, Linear Algebra, Discrete Mathematics

Projects

  1. Project title and duration:Independence polynomials of graphs and associated fractals, 2019-22. Mathematical Research Impact Centric Support (MTR/2018/000498 dated 12.03.2019), Funded by SERB, DST, Amount: Rupees 6 Lakhs. (Completed).
  2. Project title and duration:Omitted values in complex dynamics, 2014-17. Supported by the Department of Science & Technology, Govt. of India. Amount: Rupees 13.44 Lakhs (Completed).
  3.  Project title and duration: Julia sets of transcendental meromorphic functions, 21/07/2010 - 30/06/2012. Supported by  IIT Bhubaneswar. Amount: Rupees 5 Lakhs(Completed).
  4. Project title and duration: Topological aspects of transcendental  dynamics, 2009-2010. Supported by the China Postdoctoral Science Foundation (Grant no. 20090450420). Amount: RMB 30,000.(Completed). .

Recent Publications (International Journals)

1Tarakanta Nayak and Soumen Pal, The Julia sets of Chebyshev's method with small degrees, Nonlinear Dynamics(2022)
2Subhasis Ghora and Tarakanta Nayak, On Fatou sets containing Baker omitted value, Accepted, Journal of Dynamics and Differential Equations(2021)
3Tarakanta Nayak and Soumen Pal, Quadratic and cubic Newton maps of rational functions, Proceedings-Mathematical Sciences(2022), https://doi.org/10.1007/s12044-022-00688-1
4Subhasis Ghora and Tarakanta Nayak, On periods of Herman rings and relevant poles, Indian J Pure Appl Math (2021). https://doi.org/10.1007/s13226-021-00112-w.
5Sasmita Barik, Tarakanta Nayak and Ankit Pradhan, Graphs whose independent fractals are line segments, Bulletin of the Malaysian Mathematical Sciences Society, 44(1), 55-78 (2020) https://doi.org/10.1007/s40840-020-00936-5
6Tarun Kumar Chakra and Tarakanta Nayak, Iteration of the translated tangent, Bulletin of the Malaysian Mathematical Sciences Society, 42 (2019), no. 5, 1993-2008.
7Tarun Kumar Chakra, Gorachand Chakraborty and Tarakanta Nayak, Herman rings with small periods and omitted values, Acta Mathematica Scientia, Series B, 38 (2018), no. 6, 1951-1965
8Tarun Kumar Chakra, Tarakanta Nayak and Kedarnath Senapati, Iteration of certain exponential-like meromorphic functions, Proceedings of Indian Academy of Sciences (Mathematical Sciences), 128 (2018), no. 5, Art. 64, 18 pp.
9Tarun Kumar Chakra, Gorachand Chakraborty and Tarakanta Nayak, Baker omitted value, Complex Variables and Elliptic Functions, 61 (2016), no. 10, 1353 - 1361.
10Tarakanta Nayak, Herman rings of meromorphic maps with an omitted value, Proceedings of the American Mathematical Society, 144 (2016), no. 2, 587 - 597.
11Tarakanta Nayak, On Fatou components and omitted values, Geometry, groups and dynamics, 349 - 358, Contemporary Mathematics, 639, American Mathematical Society, Providence, RI, 2015.
12Tarakanta Nayak and M. Guru Prem Prasad, Julia sets of Joukowski-exponential maps, {\it Complex Analysis and Operator Theory}, 8 (2014), no.5, 1061--1076.
13Tarakanta Nayak and Jian-Hua Zheng, Omitted values and dynamics of meromorphic functions, Journal of London Mathematical Society, (2) 83 (2011), no.1, 121--136.
14Tarakanta Nayak and M. Guru Prem Prasad, Iteration of certain meromorphic functions with unbounded singular values, Ergodic Theory and Dynamical Systems, 30 (2010), no.3, 877--891.
15Tarakanta Nayak and Zheng Jian Hua, Omitted values and dynamics of meromorphic functions, Abstracts, International Congress of Mathematicians, 19–27 August, 2010, 313
16 M. Guru Prem Prasad and Tarakanta Nayak, Dynamics of $\lambda \tanh (e^z)$, Discrete and Continuous Dynamical Systems Series A, 19 (2007), no.1, 121--138.
17 M. Guru Prem Prasad and Tarakanta Nayak, Dynamics of certain class of critically bounded entire transcendental functions, Journal of Mathematical Analysis and Applications, 329 (2007), no.2, 1446--1459.
18Tarakanta Nayak and M. Guru Prem Prasad, Bifurcation and chaotic burst in the dynamics of $\lambda e^{b z + c e^z}$, Journal of Combinatorics, Information and System Sciences, 28/29 (2003/2004), 211--226.
19Subhasis Ghora and Tarakanta Nayak, Rotation domains and Stable Baker omitted value, with Subhasis Ghora, Qualitative Theory of Dynamical Systems(2021), https://doi.org/10.1007/s12346-021-00527-0

Recent Publications (National Journals)

1Tarakanta Nayak, Polynomials through pictures, Resonance (September 2021)
2Rajen Kumar and Tarakanta Nayak, The Real Non-attractive Fixed Point Conjecture and Beyond, Mathematics Newsletter, 31 (Sept 2020), no. 2, 64-71.
3Exploding Julia sets in the dynamics of f ?(z) = ?J1(iz)/iz, Proceedings of The Third National Conference on Non-linear Systems and Dynamics, (NCNSD-2006), 171-174, Allied Publishers Pvt. Ltd.

Conferences (International)

1 Baker omitted value, Invited talk in 34 th Annual Conference of the Ramanujan Mathematical Society, 1-3 August 2019, Pondicherry University, Punducherry, India
2Independence fractal of a graph, Invited talk in 83rd Annual Conference of Indian Mathematical Society, 12-15 Dec 2017, Sri Venkateswar University, Tirupati, Andhra Pradesh, India
3Completely invariant domains, Complex Analysis: Geometric and Dynamical Aspects, Non 14-19, 2016, Centre of Excellence in Mathematical Sciences, Almora, India
4Herman rings, Frontiers in Complex Dynamics, Dec 19 -- 20, 2012, University of Barcelona, Spain

Conferences (National)

1Complex Dynamics of some simple maps, National Workshop on Topological Dynamics Dec 10 -- 12, 2015, National Institute of Technology, Karnataka, Surathkal, India
 

Academic Honors & Awards

  • Ramanujan Prize for 2018 given by Ramanujan Institute for Advanced Study in Mathematics, University of Chennai
  • Member of INYAS (Indian National Young Academy of Science), 2018-2022
  • Junior Associate of International Centre for Theoretical Physics, Italy for the period 2012-2017
 

Research Scholar

PhD
Completed: 2 (Tarun Kumar Chakra and Subhasis Ghora)
Continuing: 3 (Soumen Pal, Pooja and Sukanta Das)
 
MSc projects for students of IIT Bhubaneswar
Completed: 17
Continuing: 3
 
BTech projects for students of IIT Bhubaneswar
Completed: 2
 
 
MSc and BTech projects for other students 
Completed: 7
 
 

Professional Activities

 
  • Reviewer, Mathematical Reviews (Published by American Mathematical Society)
  • Regional Coordinator (Odisha), Madhava Mathematics Competition (since 2015)
  • Acted as supervisor for Joint Science Academies' Summer Research Fellowship Programme
  • Member, Board of studies, Salipur Autonomous College, Salipur (2014-2016)
  • Zonal coordinator, Indian National Mathematical Olympiad for Utkal University zone
  • Member in the interview board for selection of Trained Graduate Teachers in Kendriya Vidyalaya Sangathan on 30 April, 2011

Sponsored projects

  1. Project title and duration: Independence polynomials of graphs and associated fractals, 14 March 2019-13 March 2022. Supported by the Department of Science & Technology, Govt. of India. Amount: Rupees 6.6 Lakhs
  2.  Project title and duration:Omitted values in complex dynamics, 2014-17. Supported by the Department of Science & Technology, Govt. of India. Amount: Rupees 13.44 Lakhs.
  3.  Project title and duration: Julia sets of transcendental meromorphic functions, 21/07/2010 - 30/06/2012. Supported by  IIT Bhubaneswar. Amount: Rupees 5 Lakhs
  4. Project title and duration: Topological aspects of transcendental  dynamics, 2009-2010. Supported by the China Postdoctoral Science Foundation (Grant no. 20090450420). Amount: RMB 30,000.

Student Supervision

       

    PhD: Soumen Pal and Sukanta Das (continuing)

     Subhasis Ghora (Thesis submitted in 2022)

    Tarun Kumar Chakra, 2018 (Thesis: Iteration of meromorphic functions with an omitted value)

    Post Doc:  Dr Kedarnath Senapati , 2014-2016 

    MSc:

    14. Dynamics of Reduced Independence polynomials,  2021-22

    13. Line segments as independence fractals, Saikat Giri, 2019-20

    12. Fixed points and their multipliers for a polynomial, Rajen Kumar, 2018-19.

    11. Graphs whose independence fractals are line segments, Sanjoy Mondal, 2018-19 

    10. Quasiconformal mapping and No wandering theorem, Abhisek Pandey,  2018-19 

     9.  Fractal Transformation using Iterated Function System, Chavan Ratan,  2017-18

    8. Quasiconformal mappings,  Garima Gupta, 2016-17

    7. A study of roots of Independence polynomials, Vijay Kumar Meena, 2016-17

    6. The Independence fractal of a graph, Kartik Pandey, 2016-17

    5. Finding all roots of a polynomial by Newton's Method, Soumen Pal, 2015-16

    4. A study on palindromic polynomials,  Priti Prasanna Mondal, 2015-16

    3. Polynomial root finding, Anudeep Nain, 2014-15

    2. The Julia sets of relaxed Newton  method for polynomials with two roots, Satyabrata Jana, 2014-15

    1. Dynamical behaviour of multiply connected Fatou components of transcendental entire functions, Jogender Singh, 2014-15.

     Summer and Winter projects:

    4. Roots of Chromatic Polynomials, winter project by Labhansh Gemini, NIT Hamirpur, 11-31 Dec 2018

    3. The independence polynomial of a graph, summer project by Satyabrat Rath, NIT Rourkela, 2018

    2. On Herman rings of transcendental meromorphic functions, summer project by Pranav Kumar Upadrasta, IIT Kharagpur (under SRF Programme - 2014,  jointly sponsored by IASc-Bangalore, INSA-New Delhi and NSAI-Allahabad).

    1. When two fractals are the same, summer project by Prashant Kumar Ojha, NIT Rourkela during May 15 -- July 15, 2011.

 

 

Professional Experience

Associate Professor, 24 February 2020 onwards, IIT Bhubaneswar Assistant Professor, May 2010 -- February 2020, IIT Bhubaneswar Postdoc,  September 2008 -- May 2010, Tsinghua University, China  Report: Omitted values and conformal measures in complex dynamics Assistant Professor,  December  2007 --  August  2008, National Institute of Technology Rourkela Postdoc, 5 February 2007 --  1 December 2007 Harish-Chandra Research Institute, Allahabad, India        

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